Simple Molecules
题意翻译
有一个具有三个顶点的无向图，给出每个顶点的度（即与这个顶点相连的边的数目）
如果有一种连接边的方式，使得每个顶点的度都等于给出的数字，请输出这种方案：
输出格式：
- 输出共$1$行，三个整数，用空格分开；
- 三个整数分别为第$1$和第$2$，第$2$和第$3$，第$3$和第$1$顶点之间的边数；
否则输出`Impossible`。
题目描述
Mad scientist Mike is busy carrying out experiments in chemistry. Today he will attempt to join three atoms into one molecule.
A molecule consists of atoms, with some pairs of atoms connected by atomic bonds. Each atom has a valence number — the number of bonds the atom must form with other atoms. An atom can form one or multiple bonds with any other atom, but it cannot form a bond with itself. The number of bonds of an atom in the molecule must be equal to its valence number.
Mike knows valence numbers of the three atoms. Find a molecule that can be built from these atoms according to the stated rules, or determine that it is impossible.
输入输出格式
输入格式
The single line of the input contains three space-separated integers $ a $ , $ b $ and $ c $ ( $ 1<=a,b,c<=10^{6} $ ) — the valence numbers of the given atoms.
输出格式
If such a molecule can be built, print three space-separated integers — the number of bonds between the 1-st and the 2-nd, the 2-nd and the 3-rd, the 3-rd and the 1-st atoms, correspondingly. If there are multiple solutions, output any of them. If there is no solution, print "Impossible" (without the quotes).
输入输出样例
输入样例 #1
1 1 2
输出样例 #1
0 1 1
输入样例 #2
3 4 5
输出样例 #2
1 3 2
输入样例 #3
4 1 1
输出样例 #3
Impossible
说明
The first sample corresponds to the first figure. There are no bonds between atoms 1 and 2 in this case.
The second sample corresponds to the second figure. There is one or more bonds between each pair of atoms.
The third sample corresponds to the third figure. There is no solution, because an atom cannot form bonds with itself.
The configuration in the fourth figure is impossible as each atom must have at least one atomic bond.